Since the Earth continuously rotates from West to East,

Is the time taken to go to America from India by a flight different to the time taken to come from there?

NO.

because when the aeroplane moves from america to india the motion of aeroplane is with respect to gravitation pull of earth.

for example when u jump  or throw a rock from a tall building like burz kalifa,the rock falls exactly down if there is no air resistance.

but this is not in the case of a space ship in space because it is out of earth''s gravity.

no it takes same time to travel from america to india. the rotation of the earth from west to east doesnt effect the time taken as we are also rotating with it